Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [63,12,Mod(37,63)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(63, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 2]))
N = Newforms(chi, 12, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("63.37");
S:= CuspForms(chi, 12);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 63 = 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 12 \) |
Character orbit: | \([\chi]\) | \(=\) | 63.e (of order \(3\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(48.4056203753\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - x^{11} + 1846 x^{10} + 9475 x^{9} + 2735534 x^{8} + 11305015 x^{7} + 1247863105 x^{6} + \cdots + 4089842896896 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{20}\cdot 3^{5}\cdot 7^{6} \) |
Twist minimal: | no (minimal twist has level 7) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 37.4 | ||
Root | \(-0.427084 + 0.739732i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 63.37 |
Dual form | 63.12.e.b.46.4 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/63\mathbb{Z}\right)^\times\).
\(n\) | \(10\) | \(29\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.85417 | + | 4.94356i | −0.0630688 | + | 0.109238i | −0.895836 | − | 0.444385i | \(-0.853422\pi\) |
0.832767 | + | 0.553624i | \(0.186755\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1007.71 | + | 1745.40i | 0.492045 | + | 0.852246i | ||||
\(5\) | 4491.11 | − | 7778.83i | 0.642716 | − | 1.11322i | −0.342108 | − | 0.939661i | \(-0.611141\pi\) |
0.984824 | − | 0.173556i | \(-0.0555257\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −43014.2 | − | 11274.1i | −0.967326 | − | 0.253538i | ||||
\(8\) | −23195.3 | −0.250268 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 25636.8 | + | 44404.2i | 0.0810706 | + | 0.140418i | ||||
\(11\) | 45694.4 | + | 79145.1i | 0.0855468 | + | 0.148171i | 0.905624 | − | 0.424081i | \(-0.139403\pi\) |
−0.820077 | + | 0.572253i | \(0.806070\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −775221. | −0.579078 | −0.289539 | − | 0.957166i | \(-0.593502\pi\) | ||||
−0.289539 | + | 0.957166i | \(0.593502\pi\) | |||||||
\(14\) | 178504. | − | 180465.i | 0.0887041 | − | 0.0896788i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −1.99758e6 | + | 3.45991e6i | −0.476261 | + | 0.824907i | ||||
\(17\) | 4.63726e6 | + | 8.03198e6i | 0.792123 | + | 1.37200i | 0.924650 | + | 0.380818i | \(0.124358\pi\) |
−0.132527 | + | 0.991179i | \(0.542309\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.43623e6 | − | 2.48762e6i | 0.133070 | − | 0.230483i | −0.791789 | − | 0.610795i | \(-0.790850\pi\) |
0.924858 | + | 0.380312i | \(0.124183\pi\) | |||||||
\(20\) | 1.81029e7 | 1.26498 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −521678. | −0.0215813 | ||||||||
\(23\) | 5.26756e6 | − | 9.12369e6i | 0.170650 | − | 0.295575i | −0.767997 | − | 0.640453i | \(-0.778747\pi\) |
0.938647 | + | 0.344879i | \(0.112080\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.59261e7 | − | 2.75848e7i | −0.326167 | − | 0.564938i | ||||
\(26\) | 2.21261e6 | − | 3.83236e6i | 0.0365218 | − | 0.0632576i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −2.36679e7 | − | 8.64380e7i | −0.259891 | − | 0.949151i | ||||
\(29\) | 4.24570e7 | 0.384380 | 0.192190 | − | 0.981358i | \(-0.438441\pi\) | ||||
0.192190 | + | 0.981358i | \(0.438441\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.29120e7 | + | 9.16463e7i | 0.331944 | + | 0.574944i | 0.982893 | − | 0.184178i | \(-0.0589622\pi\) |
−0.650949 | + | 0.759121i | \(0.725629\pi\) | |||||||
\(32\) | −3.51549e7 | − | 6.08901e7i | −0.185209 | − | 0.320791i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −5.29421e7 | −0.199833 | ||||||||
\(35\) | −2.80881e8 | + | 2.83967e8i | −0.903957 | + | 0.913890i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.54843e8 | + | 2.68196e8i | −0.367099 | + | 0.635833i | −0.989111 | − | 0.147174i | \(-0.952982\pi\) |
0.622012 | + | 0.783008i | \(0.286315\pi\) | |||||||
\(38\) | 8.19848e6 | + | 1.42002e7i | 0.0167851 | + | 0.0290726i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −1.04173e8 | + | 1.80433e8i | −0.160851 | + | 0.278603i | ||||
\(41\) | 1.19606e8 | 0.161229 | 0.0806144 | − | 0.996745i | \(-0.474312\pi\) | ||||
0.0806144 | + | 0.996745i | \(0.474312\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.16451e9 | 1.20800 | 0.604001 | − | 0.796983i | \(-0.293572\pi\) | ||||
0.604001 | + | 0.796983i | \(0.293572\pi\) | |||||||
\(44\) | −9.20932e7 | + | 1.59510e8i | −0.0841856 | + | 0.145814i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 3.00690e7 | + | 5.20811e7i | 0.0215254 | + | 0.0372831i | ||||
\(47\) | −1.25006e8 | + | 2.16517e8i | −0.0795048 | + | 0.137706i | −0.903036 | − | 0.429564i | \(-0.858667\pi\) |
0.823532 | + | 0.567270i | \(0.192001\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.72312e9 | + | 9.69892e8i | 0.871437 | + | 0.490507i | ||||
\(50\) | 1.81823e8 | 0.0822838 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −7.81196e8 | − | 1.35307e9i | −0.284932 | − | 0.493517i | ||||
\(53\) | 1.73284e9 | + | 3.00136e9i | 0.569168 | + | 0.985829i | 0.996648 | + | 0.0818038i | \(0.0260681\pi\) |
−0.427480 | + | 0.904025i | \(0.640599\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 8.20875e8 | 0.219929 | ||||||||
\(56\) | 9.97729e8 | + | 2.61506e8i | 0.242091 | + | 0.0634524i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −1.21180e8 | + | 2.09889e8i | −0.0242424 | + | 0.0419890i | ||||
\(59\) | 3.01421e9 | + | 5.22077e9i | 0.548893 | + | 0.950711i | 0.998351 | + | 0.0574095i | \(0.0182841\pi\) |
−0.449457 | + | 0.893302i | \(0.648383\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5.31834e9 | + | 9.21163e9i | −0.806236 | + | 1.39644i | 0.109218 | + | 0.994018i | \(0.465165\pi\) |
−0.915454 | + | 0.402423i | \(0.868168\pi\) | |||||||
\(62\) | −6.04079e8 | −0.0837412 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −7.78074e9 | −0.905798 | ||||||||
\(65\) | −3.48161e9 | + | 6.03032e9i | −0.372183 | + | 0.644639i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.10439e9 | − | 1.91285e9i | −0.0999332 | − | 0.173089i | 0.811724 | − | 0.584042i | \(-0.198530\pi\) |
−0.911657 | + | 0.410952i | \(0.865196\pi\) | |||||||
\(68\) | −9.34601e9 | + | 1.61878e10i | −0.779520 | + | 1.35017i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −6.02129e8 | − | 2.19904e9i | −0.0428203 | − | 0.156385i | ||||
\(71\) | 1.34122e10 | 0.882223 | 0.441111 | − | 0.897452i | \(-0.354584\pi\) | ||||
0.441111 | + | 0.897452i | \(0.354584\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 8.02494e9 | + | 1.38996e10i | 0.453071 | + | 0.784742i | 0.998575 | − | 0.0533664i | \(-0.0169951\pi\) |
−0.545504 | + | 0.838108i | \(0.683662\pi\) | |||||||
\(74\) | −8.83897e8 | − | 1.53095e9i | −0.0463049 | − | 0.0802025i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 5.78919e9 | 0.261905 | ||||||||
\(77\) | −1.07322e9 | − | 3.91953e9i | −0.0451846 | − | 0.165019i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −8.41954e9 | + | 1.45831e10i | −0.307850 | + | 0.533212i | −0.977892 | − | 0.209111i | \(-0.932943\pi\) |
0.670042 | + | 0.742323i | \(0.266276\pi\) | |||||||
\(80\) | 1.79427e10 | + | 3.10777e10i | 0.612200 | + | 1.06036i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −3.41376e8 | + | 5.91281e8i | −0.0101685 | + | 0.0176124i | ||||
\(83\) | 1.25839e10 | 0.350659 | 0.175329 | − | 0.984510i | \(-0.443901\pi\) | ||||
0.175329 | + | 0.984510i | \(0.443901\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 8.33059e10 | 2.03644 | ||||||||
\(86\) | −3.32372e9 | + | 5.75684e9i | −0.0761873 | + | 0.131960i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −1.05990e9 | − | 1.83580e9i | −0.0214096 | − | 0.0370826i | ||||
\(89\) | −3.02118e10 | + | 5.23283e10i | −0.573497 | + | 0.993326i | 0.422706 | + | 0.906267i | \(0.361080\pi\) |
−0.996203 | + | 0.0870594i | \(0.972253\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.33455e10 | + | 8.73991e9i | 0.560157 | + | 0.146818i | ||||
\(92\) | 2.12326e10 | 0.335870 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −7.13578e8 | − | 1.23595e9i | −0.0100286 | − | 0.0173700i | ||||
\(95\) | −1.29005e10 | − | 2.23444e10i | −0.171052 | − | 0.296270i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1.39153e11 | −1.64531 | −0.822654 | − | 0.568542i | \(-0.807508\pi\) | ||||
−0.822654 | + | 0.568542i | \(0.807508\pi\) | |||||||
\(98\) | −9.71279e9 | + | 5.75010e9i | −0.108543 | + | 0.0642587i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 3.20977e10 | − | 5.55949e10i | 0.320977 | − | 0.555949i | ||||
\(101\) | −7.27138e10 | − | 1.25944e11i | −0.688413 | − | 1.19237i | −0.972351 | − | 0.233524i | \(-0.924974\pi\) |
0.283938 | − | 0.958843i | \(-0.408359\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −9.52360e10 | + | 1.64954e11i | −0.809462 | + | 1.40203i | 0.103775 | + | 0.994601i | \(0.466908\pi\) |
−0.913237 | + | 0.407429i | \(0.866425\pi\) | |||||||
\(104\) | 1.79815e10 | 0.144925 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1.97833e10 | −0.143587 | ||||||||
\(107\) | −2.98014e10 | + | 5.16176e10i | −0.205412 | + | 0.355785i | −0.950264 | − | 0.311445i | \(-0.899187\pi\) |
0.744852 | + | 0.667230i | \(0.232520\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −7.38720e10 | − | 1.27950e11i | −0.459869 | − | 0.796517i | 0.539084 | − | 0.842252i | \(-0.318770\pi\) |
−0.998954 | + | 0.0457350i | \(0.985437\pi\) | |||||||
\(110\) | −2.34292e9 | + | 4.05805e9i | −0.0138707 | + | 0.0240247i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 1.24932e11 | − | 1.26304e11i | 0.669844 | − | 0.677204i | ||||
\(113\) | 2.11327e11 | 1.07901 | 0.539503 | − | 0.841984i | \(-0.318612\pi\) | ||||
0.539503 | + | 0.841984i | \(0.318612\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −4.73144e10 | − | 8.19510e10i | −0.219359 | − | 0.379941i | ||||
\(116\) | 4.27843e10 | + | 7.41046e10i | 0.189132 | + | 0.327586i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −3.44123e10 | −0.138472 | ||||||||
\(119\) | −1.08915e11 | − | 3.97770e11i | −0.418388 | − | 1.52800i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.38480e11 | − | 2.39854e11i | 0.485364 | − | 0.840674i | ||||
\(122\) | −3.03589e10 | − | 5.25831e10i | −0.101697 | − | 0.176144i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −1.06640e11 | + | 1.84705e11i | −0.326663 | + | 0.565796i | ||||
\(125\) | 1.52481e11 | 0.446901 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 3.51747e11 | 0.944735 | 0.472367 | − | 0.881402i | \(-0.343400\pi\) | ||||
0.472367 | + | 0.881402i | \(0.343400\pi\) | |||||||
\(128\) | 9.42048e10 | − | 1.63167e11i | 0.242336 | − | 0.419738i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −1.98742e10 | − | 3.44231e10i | −0.0469462 | − | 0.0813132i | ||||
\(131\) | −2.15308e10 | + | 3.72924e10i | −0.0487604 | + | 0.0844556i | −0.889375 | − | 0.457177i | \(-0.848860\pi\) |
0.840615 | + | 0.541633i | \(0.182194\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −8.98239e10 | + | 9.08109e10i | −0.187158 | + | 0.189214i | ||||
\(134\) | 1.26084e10 | 0.0252107 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1.07563e11 | − | 1.86304e11i | −0.198243 | − | 0.343368i | ||||
\(137\) | −4.92302e11 | − | 8.52692e11i | −0.871502 | − | 1.50949i | −0.860443 | − | 0.509547i | \(-0.829813\pi\) |
−0.0110587 | − | 0.999939i | \(-0.503520\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −7.31783e10 | −0.119619 | −0.0598096 | − | 0.998210i | \(-0.519049\pi\) | ||||
−0.0598096 | + | 0.998210i | \(0.519049\pi\) | |||||||
\(140\) | −7.78682e11 | − | 2.04094e11i | −1.22365 | − | 0.320720i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −3.82806e10 | + | 6.63040e10i | −0.0556407 | + | 0.0963726i | ||||
\(143\) | −3.54233e10 | − | 6.13549e10i | −0.0495383 | − | 0.0858028i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.90679e11 | − | 3.30266e11i | 0.247047 | − | 0.427898i | ||||
\(146\) | −9.16181e10 | −0.114299 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −6.24147e11 | −0.722515 | ||||||||
\(149\) | −2.21679e11 | + | 3.83960e11i | −0.247287 | + | 0.428313i | −0.962772 | − | 0.270314i | \(-0.912872\pi\) |
0.715485 | + | 0.698628i | \(0.246206\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 6.38440e11 | + | 1.10581e12i | 0.661830 | + | 1.14632i | 0.980134 | + | 0.198335i | \(0.0635534\pi\) |
−0.318304 | + | 0.947989i | \(0.603113\pi\) | |||||||
\(152\) | −3.33138e10 | + | 5.77012e10i | −0.0333031 | + | 0.0576827i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 2.24396e10 | + | 5.88145e9i | 0.0208762 | + | 0.00547168i | ||||
\(155\) | 9.50535e11 | 0.853382 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −4.66854e11 | − | 8.08615e11i | −0.390601 | − | 0.676541i | 0.601928 | − | 0.798550i | \(-0.294399\pi\) |
−0.992529 | + | 0.122010i | \(0.961066\pi\) | |||||||
\(158\) | −4.80616e10 | − | 8.32451e10i | −0.0388315 | − | 0.0672581i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −6.31538e11 | −0.476146 | ||||||||
\(161\) | −3.29441e11 | + | 3.33061e11i | −0.240014 | + | 0.242651i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1.23921e12 | − | 2.14638e12i | 0.843556 | − | 1.46108i | −0.0433132 | − | 0.999062i | \(-0.513791\pi\) |
0.886869 | − | 0.462020i | \(-0.152875\pi\) | |||||||
\(164\) | 1.20528e11 | + | 2.08761e11i | 0.0793317 | + | 0.137407i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −3.59165e10 | + | 6.22092e10i | −0.0221156 | + | 0.0383054i | ||||
\(167\) | 2.38715e12 | 1.42213 | 0.711065 | − | 0.703126i | \(-0.248213\pi\) | ||||
0.711065 | + | 0.703126i | \(0.248213\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.19119e12 | −0.664669 | ||||||||
\(170\) | −2.37769e11 | + | 4.11828e11i | −0.128436 | + | 0.222457i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 1.17349e12 | + | 2.03254e12i | 0.594391 | + | 1.02952i | ||||
\(173\) | 2.71347e11 | − | 4.69988e11i | 0.133129 | − | 0.230586i | −0.791752 | − | 0.610842i | \(-0.790831\pi\) |
0.924881 | + | 0.380256i | \(0.124164\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3.74055e11 | + | 1.36609e12i | 0.172277 | + | 0.629174i | ||||
\(176\) | −3.65113e11 | −0.162970 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −1.72459e11 | − | 2.98708e11i | −0.0723396 | − | 0.125296i | ||||
\(179\) | 1.65743e12 | + | 2.87075e12i | 0.674128 | + | 1.16762i | 0.976723 | + | 0.214505i | \(0.0688139\pi\) |
−0.302594 | + | 0.953119i | \(0.597853\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −7.57463e11 | −0.289821 | −0.144910 | − | 0.989445i | \(-0.546289\pi\) | ||||
−0.144910 | + | 0.989445i | \(0.546289\pi\) | |||||||
\(182\) | −1.38380e11 | + | 1.39901e11i | −0.0513666 | + | 0.0519310i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −1.22183e11 | + | 2.11627e11i | −0.0427083 | + | 0.0739730i | ||||
\(185\) | 1.39084e12 | + | 2.40900e12i | 0.471880 | + | 0.817320i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −4.23794e11 | + | 7.34033e11i | −0.135527 | + | 0.234740i | ||||
\(188\) | −5.03879e11 | −0.156480 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 1.47281e11 | 0.0431521 | ||||||||
\(191\) | −2.41197e12 | + | 4.17765e12i | −0.686575 | + | 1.18918i | 0.286364 | + | 0.958121i | \(0.407553\pi\) |
−0.972939 | + | 0.231062i | \(0.925780\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3.50989e11 | + | 6.07931e11i | 0.0943471 | + | 0.163414i | 0.909336 | − | 0.416063i | \(-0.136590\pi\) |
−0.814989 | + | 0.579477i | \(0.803257\pi\) | |||||||
\(194\) | 3.97166e11 | − | 6.87911e11i | 0.103768 | − | 0.179731i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 4.35469e10 | + | 3.98490e12i | 0.0107535 | + | 0.984031i | ||||
\(197\) | −3.47030e12 | −0.833302 | −0.416651 | − | 0.909066i | \(-0.636796\pi\) | ||||
−0.416651 | + | 0.909066i | \(0.636796\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1.44819e12 | + | 2.50834e12i | 0.328953 | + | 0.569764i | 0.982304 | − | 0.187291i | \(-0.0599708\pi\) |
−0.653351 | + | 0.757055i | \(0.726637\pi\) | |||||||
\(200\) | 3.69412e11 | + | 6.39840e11i | 0.0816292 | + | 0.141386i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 8.30150e11 | 0.173670 | ||||||||
\(203\) | −1.82626e12 | − | 4.78665e11i | −0.371821 | − | 0.0974548i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 5.37165e11 | − | 9.30397e11i | 0.103624 | − | 0.179482i | ||||
\(206\) | −5.43639e11 | − | 9.41611e11i | −0.102104 | − | 0.176849i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 1.54857e12 | − | 2.68220e12i | 0.275792 | − | 0.477686i | ||||
\(209\) | 2.62511e11 | 0.0455347 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2.99203e10 | −0.00492508 | −0.00246254 | − | 0.999997i | \(-0.500784\pi\) | ||||
−0.00246254 | + | 0.999997i | \(0.500784\pi\) | |||||||
\(212\) | −3.49239e12 | + | 6.04899e12i | −0.560113 | + | 0.970143i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −1.70117e11 | − | 2.94651e11i | −0.0259102 | − | 0.0448778i | ||||
\(215\) | 5.22996e12 | − | 9.05855e12i | 0.776402 | − | 1.34477i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.24274e12 | − | 4.53863e12i | −0.175328 | − | 0.640318i | ||||
\(218\) | 8.43373e11 | 0.116014 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 8.27202e11 | + | 1.43276e12i | 0.108215 | + | 0.187434i | ||||
\(221\) | −3.59491e12 | − | 6.22656e12i | −0.458701 | − | 0.794494i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −2.52256e12 | −0.306312 | −0.153156 | − | 0.988202i | \(-0.548944\pi\) | ||||
−0.153156 | + | 0.988202i | \(0.548944\pi\) | |||||||
\(224\) | 8.25680e11 | + | 3.01548e12i | 0.0978245 | + | 0.357266i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −6.03163e11 | + | 1.04471e12i | −0.0680516 | + | 0.117869i | ||||
\(227\) | 6.08276e12 | + | 1.05356e13i | 0.669820 | + | 1.16016i | 0.977954 | + | 0.208820i | \(0.0669622\pi\) |
−0.308134 | + | 0.951343i | \(0.599704\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2.17759e12 | − | 3.77170e12i | 0.228497 | − | 0.395769i | −0.728866 | − | 0.684657i | \(-0.759952\pi\) |
0.957363 | + | 0.288888i | \(0.0932854\pi\) | |||||||
\(230\) | 5.40173e11 | 0.0553388 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −9.84806e11 | −0.0961981 | ||||||||
\(233\) | 8.54463e12 | − | 1.47997e13i | 0.815147 | − | 1.41188i | −0.0940755 | − | 0.995565i | \(-0.529990\pi\) |
0.909222 | − | 0.416311i | \(-0.136677\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.12283e12 | + | 1.94481e12i | 0.102198 | + | 0.177012i | ||||
\(236\) | −6.07489e12 | + | 1.05220e13i | −0.540160 | + | 0.935585i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 2.27726e12 | + | 5.96875e11i | 0.193304 | + | 0.0506652i | ||||
\(239\) | 3.04856e11 | 0.0252876 | 0.0126438 | − | 0.999920i | \(-0.495975\pi\) | ||||
0.0126438 | + | 0.999920i | \(0.495975\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −8.33995e11 | − | 1.44452e12i | −0.0660800 | − | 0.114454i | 0.831093 | − | 0.556134i | \(-0.187716\pi\) |
−0.897173 | + | 0.441680i | \(0.854383\pi\) | |||||||
\(242\) | 7.90490e11 | + | 1.36917e12i | 0.0612226 | + | 0.106041i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −2.14373e13 | −1.58682 | ||||||||
\(245\) | 1.52833e13 | − | 9.04794e12i | 1.10613 | − | 0.654842i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.11339e12 | + | 1.92846e12i | −0.0770577 | + | 0.133468i | ||||
\(248\) | −1.22731e12 | − | 2.12577e12i | −0.0830751 | − | 0.143890i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −4.35207e11 | + | 7.53801e11i | −0.0281855 | + | 0.0488187i | ||||
\(251\) | −1.29045e13 | −0.817590 | −0.408795 | − | 0.912626i | \(-0.634051\pi\) | ||||
−0.408795 | + | 0.912626i | \(0.634051\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 9.62793e11 | 0.0583943 | ||||||||
\(254\) | −1.00395e12 | + | 1.73888e12i | −0.0595833 | + | 0.103201i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −7.42973e12 | − | 1.28687e13i | −0.422331 | − | 0.731499i | ||||
\(257\) | 1.15462e13 | − | 1.99986e13i | 0.642402 | − | 1.11267i | −0.342493 | − | 0.939520i | \(-0.611271\pi\) |
0.984895 | − | 0.173152i | \(-0.0553953\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 9.68413e12 | − | 9.79053e12i | 0.516311 | − | 0.521985i | ||||
\(260\) | −1.40338e13 | −0.732522 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −1.22905e11 | − | 2.12878e11i | −0.00615053 | − | 0.0106530i | ||||
\(263\) | −1.41565e13 | − | 2.45199e13i | −0.693746 | − | 1.20160i | −0.970601 | − | 0.240692i | \(-0.922626\pi\) |
0.276855 | − | 0.960912i | \(-0.410708\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 3.11295e13 | 1.46325 | ||||||||
\(266\) | −1.92557e11 | − | 7.03240e11i | −0.00886564 | − | 0.0323783i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 2.22580e12 | − | 3.85519e12i | 0.0983432 | − | 0.170335i | ||||
\(269\) | −1.38564e13 | − | 2.39999e13i | −0.599807 | − | 1.03890i | −0.992849 | − | 0.119376i | \(-0.961911\pi\) |
0.393042 | − | 0.919521i | \(-0.371423\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2.41659e12 | − | 4.18566e12i | 0.100432 | − | 0.173954i | −0.811431 | − | 0.584449i | \(-0.801311\pi\) |
0.911863 | + | 0.410495i | \(0.134644\pi\) | |||||||
\(272\) | −3.70533e13 | −1.50903 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 5.62045e12 | 0.219858 | ||||||||
\(275\) | 1.45547e12 | − | 2.52095e12i | 0.0558050 | − | 0.0966572i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1.89204e13 | − | 3.27711e13i | −0.697094 | − | 1.20740i | −0.969470 | − | 0.245211i | \(-0.921143\pi\) |
0.272376 | − | 0.962191i | \(-0.412191\pi\) | |||||||
\(278\) | 2.08863e11 | − | 3.61762e11i | 0.00754424 | − | 0.0130670i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 6.51513e12 | − | 6.58671e12i | 0.226232 | − | 0.228718i | ||||
\(281\) | 3.89411e13 | 1.32594 | 0.662969 | − | 0.748647i | \(-0.269296\pi\) | ||||
0.662969 | + | 0.748647i | \(0.269296\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.01150e13 | + | 1.75197e13i | 0.331238 | + | 0.573722i | 0.982755 | − | 0.184913i | \(-0.0592002\pi\) |
−0.651516 | + | 0.758634i | \(0.725867\pi\) | |||||||
\(284\) | 1.35156e13 | + | 2.34096e13i | 0.434093 | + | 0.751871i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 4.04416e11 | 0.0124973 | ||||||||
\(287\) | −5.14477e12 | − | 1.34845e12i | −0.155961 | − | 0.0408776i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2.58725e13 | + | 4.48125e13i | −0.754919 | + | 1.30756i | ||||
\(290\) | 1.08846e12 | + | 1.88527e12i | 0.0311619 | + | 0.0539740i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −1.61736e13 | + | 2.80135e13i | −0.445862 | + | 0.772256i | ||||
\(293\) | −1.09986e13 | −0.297554 | −0.148777 | − | 0.988871i | \(-0.547534\pi\) | ||||
−0.148777 | + | 0.988871i | \(0.547534\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 5.41487e13 | 1.41113 | ||||||||
\(296\) | 3.59164e12 | − | 6.22090e12i | 0.0918731 | − | 0.159129i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −1.26542e12 | − | 2.19177e12i | −0.0311922 | − | 0.0540264i | ||||
\(299\) | −4.08353e12 | + | 7.07287e12i | −0.0988197 | + | 0.171161i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −5.00906e13 | − | 1.31288e13i | −1.16853 | − | 0.306274i | ||||
\(302\) | −7.28886e12 | −0.166963 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 5.73797e12 | + | 9.93845e12i | 0.126752 | + | 0.219540i | ||||
\(305\) | 4.77705e13 | + | 8.27410e13i | 1.03636 | + | 1.79503i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1.77123e13 | −0.370692 | −0.185346 | − | 0.982673i | \(-0.559341\pi\) | ||||
−0.185346 | + | 0.982673i | \(0.559341\pi\) | |||||||
\(308\) | 5.75965e12 | − | 5.82293e12i | 0.118404 | − | 0.119705i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −2.71299e12 | + | 4.69903e12i | −0.0538218 | + | 0.0932221i | ||||
\(311\) | 7.97859e12 | + | 1.38193e13i | 0.155505 | + | 0.269342i | 0.933243 | − | 0.359246i | \(-0.116966\pi\) |
−0.777738 | + | 0.628589i | \(0.783633\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.52684e13 | − | 2.64456e13i | 0.287276 | − | 0.497577i | −0.685882 | − | 0.727712i | \(-0.740584\pi\) |
0.973159 | + | 0.230136i | \(0.0739169\pi\) | |||||||
\(314\) | 5.32992e12 | 0.0985389 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −3.39377e13 | −0.605904 | ||||||||
\(317\) | 1.70577e13 | − | 2.95449e13i | 0.299292 | − | 0.518390i | −0.676682 | − | 0.736276i | \(-0.736583\pi\) |
0.975974 | + | 0.217886i | \(0.0699161\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.94005e12 | + | 3.36027e12i | 0.0328825 | + | 0.0569541i | ||||
\(320\) | −3.49442e13 | + | 6.05251e13i | −0.582170 | + | 1.00835i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −7.06228e11 | − | 2.57923e12i | −0.0113694 | − | 0.0415224i | ||||
\(323\) | 2.66407e13 | 0.421630 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.23463e13 | + | 2.13844e13i | 0.188876 | + | 0.327143i | ||||
\(326\) | 7.07384e12 | + | 1.22523e13i | 0.106404 | + | 0.184297i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −2.77431e12 | −0.0403504 | ||||||||
\(329\) | 7.81808e12 | − | 7.90398e12i | 0.111821 | − | 0.113049i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.39115e13 | − | 2.40955e13i | 0.192451 | − | 0.333335i | −0.753611 | − | 0.657321i | \(-0.771690\pi\) |
0.946062 | + | 0.323986i | \(0.105023\pi\) | |||||||
\(332\) | 1.26809e13 | + | 2.19639e13i | 0.172540 | + | 0.298848i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −6.81333e12 | + | 1.18010e13i | −0.0896920 | + | 0.155351i | ||||
\(335\) | −1.98397e13 | −0.256914 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 8.74273e12 | 0.109568 | 0.0547839 | − | 0.998498i | \(-0.482553\pi\) | ||||
0.0547839 | + | 0.998498i | \(0.482553\pi\) | |||||||
\(338\) | 3.39986e12 | − | 5.88874e12i | 0.0419199 | − | 0.0726073i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 8.39480e13 | + | 1.45402e14i | 1.00202 | + | 1.73555i | ||||
\(341\) | −4.83557e12 | + | 8.37545e12i | −0.0567935 | + | 0.0983692i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −6.31838e13 | − | 6.11457e13i | −0.718602 | − | 0.695422i | ||||
\(344\) | −2.70113e13 | −0.302325 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 1.54894e12 | + | 2.68285e12i | 0.0167926 | + | 0.0290856i | ||||
\(347\) | 5.57163e13 | + | 9.65034e13i | 0.594525 | + | 1.02975i | 0.993614 | + | 0.112835i | \(0.0359931\pi\) |
−0.399089 | + | 0.916912i | \(0.630674\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2.49619e13 | 0.258070 | 0.129035 | − | 0.991640i | \(-0.458812\pi\) | ||||
0.129035 | + | 0.991640i | \(0.458812\pi\) | |||||||
\(350\) | −7.82098e12 | − | 2.04989e12i | −0.0795952 | − | 0.0208620i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 3.21277e12 | − | 5.56467e12i | 0.0316880 | − | 0.0548852i | ||||
\(353\) | −4.46527e13 | − | 7.73407e13i | −0.433597 | − | 0.751012i | 0.563583 | − | 0.826060i | \(-0.309423\pi\) |
−0.997180 | + | 0.0750472i | \(0.976089\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 6.02356e13 | − | 1.04331e14i | 0.567019 | − | 0.982105i | ||||
\(356\) | −1.21779e14 | −1.12874 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −1.89223e13 | −0.170066 | ||||||||
\(359\) | −8.39570e13 | + | 1.45418e14i | −0.743083 | + | 1.28706i | 0.208002 | + | 0.978128i | \(0.433304\pi\) |
−0.951085 | + | 0.308929i | \(0.900029\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 5.41196e13 | + | 9.37379e13i | 0.464585 | + | 0.804685i | ||||
\(362\) | 2.16193e12 | − | 3.74457e12i | 0.0182786 | − | 0.0316595i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 1.83479e13 | + | 6.70086e13i | 0.150497 | + | 0.549633i | ||||
\(365\) | 1.44164e14 | 1.16478 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1.03952e13 | − | 1.80050e13i | −0.0815021 | − | 0.141166i | 0.822393 | − | 0.568919i | \(-0.192638\pi\) |
−0.903895 | + | 0.427754i | \(0.859305\pi\) | |||||||
\(368\) | 2.10448e13 | + | 3.64506e13i | 0.162548 | + | 0.281541i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −1.58787e13 | −0.119044 | ||||||||
\(371\) | −4.06990e13 | − | 1.48637e14i | −0.300627 | − | 1.09792i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −6.86233e13 | + | 1.18859e14i | −0.492122 | + | 0.852381i | −0.999959 | − | 0.00907250i | \(-0.997112\pi\) |
0.507836 | + | 0.861454i | \(0.330445\pi\) | |||||||
\(374\) | −2.41916e12 | − | 4.19011e12i | −0.0170951 | − | 0.0296095i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 2.89956e12 | − | 5.02219e12i | 0.0198975 | − | 0.0344635i | ||||
\(377\) | −3.29136e13 | −0.222586 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −5.43469e12 | −0.0356992 | −0.0178496 | − | 0.999841i | \(-0.505682\pi\) | ||||
−0.0178496 | + | 0.999841i | \(0.505682\pi\) | |||||||
\(380\) | 2.59999e13 | − | 4.50332e13i | 0.168330 | − | 0.291557i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −1.37683e13 | − | 2.38474e13i | −0.0866029 | − | 0.150001i | ||||
\(383\) | 1.10671e14 | − | 1.91687e14i | 0.686183 | − | 1.18850i | −0.286881 | − | 0.957966i | \(-0.592618\pi\) |
0.973063 | − | 0.230537i | \(-0.0740484\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −3.53093e13 | − | 9.25462e12i | −0.212743 | − | 0.0557603i | ||||
\(386\) | −4.00713e12 | −0.0238014 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −1.40225e14 | − | 2.42877e14i | −0.809565 | − | 1.40221i | ||||
\(389\) | 5.67324e13 | + | 9.82634e13i | 0.322930 | + | 0.559331i | 0.981091 | − | 0.193546i | \(-0.0619989\pi\) |
−0.658161 | + | 0.752877i | \(0.728666\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 9.77083e13 | 0.540704 | ||||||||
\(392\) | −3.99683e13 | − | 2.24970e13i | −0.218093 | − | 0.122758i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 9.90481e12 | − | 1.71556e13i | 0.0525554 | − | 0.0910286i | ||||
\(395\) | 7.56262e13 | + | 1.30988e14i | 0.395720 | + | 0.685407i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 6.27094e13 | − | 1.08616e14i | 0.319143 | − | 0.552771i | −0.661167 | − | 0.750239i | \(-0.729938\pi\) |
0.980309 | + | 0.197468i | \(0.0632718\pi\) | |||||||
\(398\) | −1.65335e13 | −0.0829868 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1.27255e14 | 0.621362 | ||||||||
\(401\) | −2.01310e13 | + | 3.48679e13i | −0.0969552 | + | 0.167931i | −0.910423 | − | 0.413679i | \(-0.864244\pi\) |
0.813468 | + | 0.581610i | \(0.197577\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −4.10185e13 | − | 7.10461e13i | −0.192222 | − | 0.332937i | ||||
\(404\) | 1.46548e14 | − | 2.53829e14i | 0.677460 | − | 1.17340i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 7.57875e12 | − | 7.66202e12i | 0.0340961 | − | 0.0344707i | ||||
\(407\) | −2.83019e13 | −0.125616 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 9.79564e13 | + | 1.69665e14i | 0.423209 | + | 0.733019i | 0.996251 | − | 0.0865068i | \(-0.0275704\pi\) |
−0.573043 | + | 0.819525i | \(0.694237\pi\) | |||||||
\(410\) | 3.06632e12 | + | 5.31102e12i | 0.0130709 | + | 0.0226395i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −3.83880e14 | −1.59317 | ||||||||
\(413\) | −7.07945e13 | − | 2.58550e14i | −0.289918 | − | 1.05881i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 5.65156e13 | − | 9.78878e13i | 0.225374 | − | 0.390359i | ||||
\(416\) | 2.72528e13 | + | 4.72033e13i | 0.107250 | + | 0.185763i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −7.49250e11 | + | 1.29774e12i | −0.00287182 | + | 0.00497414i | ||||
\(419\) | −3.11107e14 | −1.17688 | −0.588441 | − | 0.808541i | \(-0.700258\pi\) | ||||
−0.588441 | + | 0.808541i | \(0.700258\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −3.15409e14 | −1.16231 | −0.581155 | − | 0.813793i | \(-0.697399\pi\) | ||||
−0.581155 | + | 0.813793i | \(0.697399\pi\) | |||||||
\(422\) | 8.53977e10 | − | 1.47913e11i | 0.000310619 | − | 0.000538008i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −4.01938e13 | − | 6.96177e13i | −0.142445 | − | 0.246722i | ||||
\(425\) | 1.47707e14 | − | 2.55836e14i | 0.516729 | − | 0.895001i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 3.32617e14 | − | 3.36272e14i | 1.13394 | − | 1.14640i | ||||
\(428\) | −1.20125e14 | −0.404288 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 2.98544e13 | + | 5.17093e13i | 0.0979335 | + | 0.169626i | ||||
\(431\) | −2.45551e14 | − | 4.25307e14i | −0.795274 | − | 1.37746i | −0.922665 | − | 0.385603i | \(-0.873994\pi\) |
0.127391 | − | 0.991853i | \(-0.459340\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −4.66688e14 | −1.47348 | −0.736739 | − | 0.676178i | \(-0.763635\pi\) | ||||
−0.736739 | + | 0.676178i | \(0.763635\pi\) | |||||||
\(434\) | 2.59840e13 | + | 6.81044e12i | 0.0810050 | + | 0.0212316i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 1.48883e14 | − | 2.57873e14i | 0.452552 | − | 0.783844i | ||||
\(437\) | −1.51309e13 | − | 2.62074e13i | −0.0454167 | − | 0.0786640i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −1.39073e14 | + | 2.40882e14i | −0.407088 | + | 0.705098i | −0.994562 | − | 0.104145i | \(-0.966789\pi\) |
0.587474 | + | 0.809243i | \(0.300123\pi\) | |||||||
\(440\) | −1.90405e13 | −0.0550412 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 4.10419e13 | 0.115719 | ||||||||
\(443\) | −2.19620e14 | + | 3.80393e14i | −0.611578 | + | 1.05928i | 0.379397 | + | 0.925234i | \(0.376131\pi\) |
−0.990975 | + | 0.134049i | \(0.957202\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2.71369e14 | + | 4.70025e14i | 0.737191 | + | 1.27685i | ||||
\(446\) | 7.19980e12 | − | 1.24704e13i | 0.0193187 | − | 0.0334611i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 3.34682e14 | + | 8.77208e13i | 0.876201 | + | 0.229654i | ||||
\(449\) | 8.42239e13 | 0.217811 | 0.108906 | − | 0.994052i | \(-0.465265\pi\) | ||||
0.108906 | + | 0.994052i | \(0.465265\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 5.46534e12 | + | 9.46624e12i | 0.0137926 | + | 0.0238895i | ||||
\(452\) | 2.12956e14 | + | 3.68850e14i | 0.530919 | + | 0.919578i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −6.94449e13 | −0.168979 | ||||||||
\(455\) | 2.17745e14 | − | 2.20137e14i | 0.523462 | − | 0.529214i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −9.06110e13 | + | 1.56943e14i | −0.212638 | + | 0.368300i | −0.952539 | − | 0.304415i | \(-0.901539\pi\) |
0.739901 | + | 0.672716i | \(0.234872\pi\) | |||||||
\(458\) | 1.24304e13 | + | 2.15301e13i | 0.0288221 | + | 0.0499214i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 9.53582e13 | − | 1.65165e14i | 0.215869 | − | 0.373896i | ||||
\(461\) | −2.32317e14 | −0.519668 | −0.259834 | − | 0.965653i | \(-0.583668\pi\) | ||||
−0.259834 | + | 0.965653i | \(0.583668\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 4.85865e14 | 1.06126 | 0.530628 | − | 0.847605i | \(-0.321956\pi\) | ||||
0.530628 | + | 0.847605i | \(0.321956\pi\) | |||||||
\(464\) | −8.48114e13 | + | 1.46898e14i | −0.183065 | + | 0.317078i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 4.87756e13 | + | 8.44819e13i | 0.102821 | + | 0.178091i | ||||
\(467\) | 4.71057e13 | − | 8.15895e13i | 0.0981365 | − | 0.169977i | −0.812777 | − | 0.582575i | \(-0.802045\pi\) |
0.910913 | + | 0.412598i | \(0.135378\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2.59386e13 | + | 9.47308e13i | 0.0527832 | + | 0.192771i | ||||
\(470\) | −1.28190e13 | −0.0257820 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −6.99157e13 | − | 1.21098e14i | −0.137371 | − | 0.237933i | ||||
\(473\) | 5.32118e13 | + | 9.21655e13i | 0.103341 | + | 0.178991i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −9.14942e13 | −0.173612 | ||||||||
\(476\) | 5.84514e14 | − | 5.90936e14i | 1.09637 | − | 1.10841i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −8.70111e11 | + | 1.50708e12i | −0.00159486 | + | 0.00276237i | ||||
\(479\) | 3.21363e14 | + | 5.56617e14i | 0.582305 | + | 1.00858i | 0.995205 | + | 0.0978061i | \(0.0311825\pi\) |
−0.412900 | + | 0.910776i | \(0.635484\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.20038e14 | − | 2.07911e14i | 0.212579 | − | 0.368197i | ||||
\(482\) | 9.52145e12 | 0.0166703 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 5.58189e14 | 0.955282 | ||||||||
\(485\) | −6.24951e14 | + | 1.08245e15i | −1.05747 | + | 1.83158i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −4.11872e14 | − | 7.13383e14i | −0.681323 | − | 1.18009i | −0.974577 | − | 0.224051i | \(-0.928072\pi\) |
0.293255 | − | 0.956034i | \(-0.405262\pi\) | |||||||
\(488\) | 1.23361e14 | − | 2.13667e14i | 0.201775 | − | 0.349485i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 1.10786e12 | + | 1.01379e14i | 0.00177177 | + | 0.162132i | ||||
\(491\) | 7.05003e14 | 1.11492 | 0.557459 | − | 0.830204i | \(-0.311776\pi\) | ||||
0.557459 | + | 0.830204i | \(0.311776\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.96885e14 | + | 3.41014e14i | 0.304476 | + | 0.527369i | ||||
\(494\) | −6.35563e12 | − | 1.10083e13i | −0.00971987 | − | 0.0168353i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −4.22784e14 | −0.632367 | ||||||||
\(497\) | −5.76914e14 | − | 1.51210e14i | −0.853397 | − | 0.223677i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −4.11492e14 | + | 7.12725e14i | −0.595399 | + | 1.03126i | 0.398091 | + | 0.917346i | \(0.369673\pi\) |
−0.993490 | + | 0.113916i | \(0.963661\pi\) | |||||||
\(500\) | 1.53657e14 | + | 2.66141e14i | 0.219895 | + | 0.380870i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 3.68316e13 | − | 6.37942e13i | 0.0515644 | − | 0.0893122i | ||||
\(503\) | −1.18063e15 | −1.63489 | −0.817445 | − | 0.576007i | \(-0.804610\pi\) | ||||
−0.817445 | + | 0.576007i | \(0.804610\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1.30626e15 | −1.76982 | ||||||||
\(506\) | −2.74797e12 | + | 4.75963e12i | −0.00368286 | + | 0.00637889i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 3.54458e14 | + | 6.13939e14i | 0.464852 | + | 0.805147i | ||||
\(509\) | 3.07502e14 | − | 5.32609e14i | 0.398933 | − | 0.690972i | −0.594661 | − | 0.803976i | \(-0.702714\pi\) |
0.993595 | + | 0.113004i | \(0.0360472\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.88481e14 | − | 6.88354e14i | −0.239305 | − | 0.873971i | ||||
\(512\) | 4.70686e14 | 0.591216 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 6.59096e13 | + | 1.14159e14i | 0.0810310 | + | 0.140350i | ||||
\(515\) | 8.55431e14 | + | 1.48165e15i | 1.04051 | + | 1.80221i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −2.28484e13 | −0.0272055 | ||||||||
\(518\) | 2.07600e13 | + | 7.58179e13i | 0.0244576 | + | 0.0893220i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 8.07570e13 | − | 1.39875e14i | 0.0931455 | − | 0.161333i | ||||
\(521\) | 1.98750e14 | + | 3.44245e14i | 0.226830 | + | 0.392880i | 0.956867 | − | 0.290527i | \(-0.0938306\pi\) |
−0.730037 | + | 0.683407i | \(0.760497\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −4.29122e14 | + | 7.43262e14i | −0.479537 | + | 0.830582i | −0.999725 | − | 0.0234698i | \(-0.992529\pi\) |
0.520188 | + | 0.854052i | \(0.325862\pi\) | |||||||
\(524\) | −8.67869e13 | −0.0959693 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 1.61621e14 | 0.175015 | ||||||||
\(527\) | −4.90734e14 | + | 8.49976e14i | −0.525881 | + | 0.910853i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 4.20910e14 | + | 7.29038e14i | 0.441757 | + | 0.765146i | ||||
\(530\) | −8.88488e13 | + | 1.53891e14i | −0.0922857 | + | 0.159843i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −2.49018e14 | − | 6.52679e13i | −0.253347 | − | 0.0664027i | ||||
\(533\) | −9.27213e13 | −0.0933640 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 2.67683e14 | + | 4.63641e14i | 0.264044 | + | 0.457337i | ||||
\(536\) | 2.56166e13 | + | 4.43693e13i | 0.0250101 | + | 0.0433188i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 1.58194e14 | 0.151316 | ||||||||
\(539\) | 1.97463e12 | + | 1.80695e14i | 0.00186960 | + | 0.171083i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −3.29697e13 | + | 5.71052e13i | −0.0305865 | + | 0.0529774i | −0.880913 | − | 0.473277i | \(-0.843071\pi\) |
0.850327 | + | 0.526255i | \(0.176404\pi\) | |||||||
\(542\) | 1.37947e13 | + | 2.38932e13i | 0.0126683 | + | 0.0219421i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 3.26045e14 | − | 5.64727e14i | 0.293416 | − | 0.508211i | ||||
\(545\) | −1.32707e15 | −1.18226 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1.54397e15 | 1.34805 | 0.674027 | − | 0.738706i | \(-0.264563\pi\) | ||||
0.674027 | + | 0.738706i | \(0.264563\pi\) | |||||||
\(548\) | 9.92192e14 | − | 1.71853e15i | 0.857636 | − | 1.48547i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 8.30831e12 | + | 1.43904e13i | 0.00703911 | + | 0.0121921i | ||||
\(551\) | 6.09780e13 | − | 1.05617e14i | 0.0511493 | − | 0.0885932i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 5.26571e14 | − | 5.32356e14i | 0.432981 | − | 0.437738i | ||||
\(554\) | 2.16008e14 | 0.175859 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −7.37423e13 | − | 1.27725e14i | −0.0588580 | − | 0.101945i | ||||
\(557\) | 1.07657e15 | + | 1.86467e15i | 0.850822 | + | 1.47367i | 0.880468 | + | 0.474106i | \(0.157229\pi\) |
−0.0296461 | + | 0.999560i | \(0.509438\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −9.02755e14 | −0.699528 | ||||||||
\(560\) | −4.21419e14 | − | 1.53907e15i | −0.323355 | − | 1.18093i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −1.11144e14 | + | 1.92508e14i | −0.0836253 | + | 0.144843i | ||||
\(563\) | −7.40273e14 | − | 1.28219e15i | −0.551564 | − | 0.955336i | −0.998162 | − | 0.0606018i | \(-0.980698\pi\) |
0.446598 | − | 0.894735i | \(-0.352635\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 9.49094e14 | − | 1.64388e15i | 0.693494 | − | 1.20117i | ||||
\(566\) | −1.15480e14 | −0.0835633 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −3.11100e14 | −0.220792 | ||||||||
\(569\) | 7.54590e14 | − | 1.30699e15i | 0.530388 | − | 0.918659i | −0.468984 | − | 0.883207i | \(-0.655380\pi\) |
0.999371 | − | 0.0354518i | \(-0.0112870\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.11735e15 | + | 1.93530e15i | 0.770352 | + | 1.33429i | 0.937370 | + | 0.348335i | \(0.113253\pi\) |
−0.167018 | + | 0.985954i | \(0.553414\pi\) | |||||||
\(572\) | 7.13926e13 | − | 1.23656e14i | 0.0487501 | − | 0.0844376i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 2.13502e13 | − | 2.15848e13i | 0.0143017 | − | 0.0144588i | ||||
\(575\) | −3.35567e14 | −0.222642 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −1.10810e15 | − | 1.91928e15i | −0.721293 | − | 1.24932i | −0.960482 | − | 0.278343i | \(-0.910215\pi\) |
0.239189 | − | 0.970973i | \(-0.423119\pi\) | |||||||
\(578\) | −1.47689e14 | − | 2.55805e14i | −0.0952237 | − | 0.164932i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 7.68596e14 | 0.486233 | ||||||||
\(581\) | −5.41285e14 | − | 1.41872e14i | −0.339201 | − | 0.0889052i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.58362e14 | + | 2.74291e14i | −0.0973810 | + | 0.168669i | ||||
\(584\) | −1.86141e14 | − | 3.22406e14i | −0.113389 | − | 0.196396i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 3.13919e13 | − | 5.43724e13i | 0.0187664 | − | 0.0325043i | ||||
\(587\) | −9.98055e14 | −0.591078 | −0.295539 | − | 0.955331i | \(-0.595499\pi\) | ||||
−0.295539 | + | 0.955331i | \(0.595499\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3.03975e14 | 0.176687 | ||||||||
\(590\) | −1.54549e14 | + | 2.67688e14i | −0.0889983 | + | 0.154150i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −6.18624e14 | − | 1.07149e15i | −0.349669 | − | 0.605645i | ||||
\(593\) | −4.92960e13 | + | 8.53833e13i | −0.0276065 | + | 0.0478159i | −0.879499 | − | 0.475902i | \(-0.842122\pi\) |
0.851892 | + | 0.523717i | \(0.175455\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −3.58334e15 | − | 9.39198e14i | −1.96990 | − | 0.516314i | ||||
\(596\) | −8.93552e14 | −0.486705 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −2.33101e13 | − | 4.03743e13i | −0.0124649 | − | 0.0215898i | ||||
\(599\) | 2.95594e14 | + | 5.11985e14i | 0.156621 | + | 0.271275i | 0.933648 | − | 0.358192i | \(-0.116607\pi\) |
−0.777027 | + | 0.629467i | \(0.783273\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 7.05336e14 | 0.366932 | 0.183466 | − | 0.983026i | \(-0.441268\pi\) | ||||
0.183466 | + | 0.983026i | \(0.441268\pi\) | |||||||
\(602\) | 2.07870e14 | − | 2.10154e14i | 0.107155 | − | 0.108332i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −1.28672e15 | + | 2.22867e15i | −0.651300 | + | 1.12808i | ||||
\(605\) | −1.24386e15 | − | 2.15442e15i | −0.623901 | − | 1.08063i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 9.23697e13 | − | 1.59989e14i | 0.0454980 | − | 0.0788048i | −0.842380 | − | 0.538885i | \(-0.818846\pi\) |
0.887878 | + | 0.460080i | \(0.152179\pi\) | |||||||
\(608\) | −2.01962e14 | −0.0985825 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −5.45380e14 | −0.261448 | ||||||||
\(611\) | 9.69075e13 | − | 1.67849e14i | 0.0460395 | − | 0.0797428i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −6.30271e14 | − | 1.09166e15i | −0.294100 | − | 0.509396i | 0.680675 | − | 0.732585i | \(-0.261687\pi\) |
−0.974775 | + | 0.223189i | \(0.928353\pi\) | |||||||
\(614\) | 5.05539e13 | − | 8.75618e13i | 0.0233791 | − | 0.0404938i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 2.48937e13 | + | 9.09147e13i | 0.0113083 | + | 0.0412991i | ||||
\(617\) | 3.07915e15 | 1.38632 | 0.693159 | − | 0.720784i | \(-0.256218\pi\) | ||||
0.693159 | + | 0.720784i | \(0.256218\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1.11640e15 | + | 1.93367e15i | 0.493768 | + | 0.855230i | 0.999974 | − | 0.00718174i | \(-0.00228604\pi\) |
−0.506207 | + | 0.862412i | \(0.668953\pi\) | |||||||
\(620\) | 9.57861e14 | + | 1.65906e15i | 0.419902 | + | 0.727292i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −9.10889e13 | −0.0392300 | ||||||||
\(623\) | 1.88949e15 | − | 1.91025e15i | 0.806604 | − | 0.815467i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.46245e15 | − | 2.53304e15i | 0.613397 | − | 1.06244i | ||||
\(626\) | 8.71571e13 | + | 1.50961e14i | 0.0362363 | + | 0.0627631i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 9.40905e14 | − | 1.62970e15i | 0.384386 | − | 0.665776i | ||||
\(629\) | −2.87220e15 | −1.16315 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −3.18888e15 | −1.26905 | −0.634523 | − | 0.772904i | \(-0.718803\pi\) | ||||
−0.634523 | + | 0.772904i | \(0.718803\pi\) | |||||||
\(632\) | 1.95294e14 | − | 3.38259e14i | 0.0770451 | − | 0.133446i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 9.73713e13 | + | 1.68652e14i | 0.0377520 | + | 0.0653884i | ||||
\(635\) | 1.57974e15 | − | 2.73618e15i | 0.607196 | − | 1.05169i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.33580e15 | − | 7.51881e14i | −0.504630 | − | 0.284042i | ||||
\(638\) | −2.21489e13 | −0.00829543 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −8.46168e14 | − | 1.46561e15i | −0.311506 | − | 0.539545i | ||||
\(641\) | −5.28395e14 | − | 9.15207e14i | −0.192859 | − | 0.334041i | 0.753338 | − | 0.657634i | \(-0.228443\pi\) |
−0.946196 | + | 0.323593i | \(0.895109\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 2.86505e15 | 1.02795 | 0.513975 | − | 0.857805i | \(-0.328172\pi\) | ||||
0.513975 | + | 0.857805i | \(0.328172\pi\) | |||||||
\(644\) | −9.13305e14 | − | 2.39379e14i | −0.324896 | − | 0.0851557i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −7.60370e13 | + | 1.31700e14i | −0.0265917 | + | 0.0460582i | ||||
\(647\) | 2.19873e14 | + | 3.80831e14i | 0.0762428 | + | 0.132056i | 0.901626 | − | 0.432516i | \(-0.142374\pi\) |
−0.825383 | + | 0.564573i | \(0.809041\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −2.75466e14 | + | 4.77120e14i | −0.0939121 | + | 0.162661i | ||||
\(650\) | −1.40953e14 | −0.0476488 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 4.99505e15 | 1.66027 | ||||||||
\(653\) | −2.92912e14 | + | 5.07338e14i | −0.0965415 | + | 0.167215i | −0.910251 | − | 0.414057i | \(-0.864111\pi\) |
0.813709 | + | 0.581272i | \(0.197445\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1.93394e14 | + | 3.34969e14i | 0.0626782 | + | 0.108562i | ||||
\(656\) | −2.38923e14 | + | 4.13827e14i | −0.0767869 | + | 0.132999i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 1.67597e13 | + | 6.12085e13i | 0.00529694 | + | 0.0193450i | ||||
\(659\) | 5.89551e14 | 0.184779 | 0.0923893 | − | 0.995723i | \(-0.470550\pi\) | ||||
0.0923893 | + | 0.995723i | \(0.470550\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 2.16762e15 | + | 3.75442e15i | 0.668151 | + | 1.15727i | 0.978421 | + | 0.206623i | \(0.0662474\pi\) |
−0.310269 | + | 0.950649i | \(0.600419\pi\) | |||||||
\(662\) | 7.94117e13 | + | 1.37545e14i | 0.0242753 | + | 0.0420461i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −2.91887e14 | −0.0877588 | ||||||||
\(665\) | 3.02993e14 | + | 1.10657e15i | 0.0903471 | + | 0.329958i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 2.23645e14 | − | 3.87365e14i | 0.0655945 | − | 0.113613i | ||||
\(668\) | 2.40555e15 | + | 4.16653e15i | 0.699751 | + | 1.21200i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 5.66258e13 | − | 9.80788e13i | 0.0162033 | − | 0.0280649i | ||||
\(671\) | −9.72074e14 | −0.275883 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1.69410e15 | 0.472994 | 0.236497 | − | 0.971632i | \(-0.424001\pi\) | ||||
0.236497 | + | 0.971632i | \(0.424001\pi\) | |||||||
\(674\) | −2.49532e13 | + | 4.32202e13i | −0.00691030 | + | 0.0119690i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −1.20037e15 | − | 2.07911e15i | −0.327047 | − | 0.566461i | ||||
\(677\) | −2.59774e15 | + | 4.49941e15i | −0.702033 | + | 1.21596i | 0.265718 | + | 0.964051i | \(0.414391\pi\) |
−0.967752 | + | 0.251907i | \(0.918942\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 5.98555e15 | + | 1.56882e15i | 1.59155 | + | 0.417148i | ||||
\(680\) | −1.93231e15 | −0.509656 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −2.76030e13 | − | 4.78099e13i | −0.00716379 | − | 0.0124081i | ||||
\(683\) | −1.70845e14 | − | 2.95913e14i | −0.0439834 | − | 0.0761815i | 0.843196 | − | 0.537607i | \(-0.180672\pi\) |
−0.887179 | + | 0.461425i | \(0.847338\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −8.84393e15 | −2.24051 | ||||||||
\(686\) | 4.82615e14 | − | 1.37833e14i | 0.121288 | − | 0.0346395i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −2.32621e15 | + | 4.02911e15i | −0.575324 | + | 0.996490i | ||||
\(689\) | −1.34333e15 | − | 2.32672e15i | −0.329593 | − | 0.570872i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −2.58334e15 | + | 4.47447e15i | −0.623810 | + | 1.08047i | 0.364960 | + | 0.931023i | \(0.381083\pi\) |
−0.988770 | + | 0.149447i | \(0.952251\pi\) | |||||||
\(692\) | 1.09376e15 | 0.262021 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −6.36094e14 | −0.149984 | ||||||||
\(695\) | −3.28652e14 | + | 5.69242e14i | −0.0768811 | + | 0.133162i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 5.54646e14 | + | 9.60674e14i | 0.127713 | + | 0.221206i | ||||
\(698\) | −7.12455e13 | + | 1.23401e14i | −0.0162762 | + | 0.0281912i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −2.00744e15 | + | 2.02950e15i | −0.451444 | + | 0.456404i | ||||
\(701\) | −3.33033e15 | −0.743084 | −0.371542 | − | 0.928416i | \(-0.621171\pi\) | ||||
−0.371542 | + | 0.928416i | \(0.621171\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 4.44781e14 | + | 7.70382e14i | 0.0976993 | + | 0.169220i | ||||
\(704\) | −3.55537e14 | − | 6.15807e14i | −0.0774880 | − | 0.134213i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 5.09785e14 | 0.109386 | ||||||||
\(707\) | 1.70782e15 | + | 6.23716e15i | 0.363610 | + | 1.32795i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 7.09927e14 | − | 1.22963e15i | 0.148819 | − | 0.257763i | −0.781972 | − | 0.623313i | \(-0.785786\pi\) |
0.930791 | + | 0.365551i | \(0.119119\pi\) | |||||||
\(710\) | 3.43845e14 | + | 5.95557e14i | 0.0715224 | + | 0.123880i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 7.00773e14 | − | 1.21377e15i | 0.143528 | − | 0.248598i | ||||
\(713\) | 1.11487e15 | 0.226585 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −6.36360e14 | −0.127356 | ||||||||
\(716\) | −3.34040e15 | + | 5.78575e15i | −0.663403 | + | 1.14905i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −4.79255e14 | − | 8.30094e14i | −0.0937307 | − | 0.162346i | ||||
\(719\) | 4.37317e15 | − | 7.57456e15i | 0.848765 | − | 1.47010i | −0.0335454 | − | 0.999437i | \(-0.510680\pi\) |
0.882311 | − | 0.470667i | \(-0.155987\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 5.95620e15 | − | 6.02165e15i | 1.13848 | − | 1.15099i | ||||
\(722\) | −6.17866e14 | −0.117203 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −7.63301e14 | − | 1.32208e15i | −0.142605 | − | 0.246999i | ||||
\(725\) | −6.76176e14 | − | 1.17117e15i | −0.125372 | − | 0.217151i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −7.92864e14 | −0.144797 | −0.0723984 | − | 0.997376i | \(-0.523065\pi\) | ||||
−0.0723984 | + | 0.997376i | \(0.523065\pi\) | |||||||
\(728\) | −7.73461e14 | − | 2.02725e14i | −0.140190 | − | 0.0367439i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −4.11467e14 | + | 7.12682e14i | −0.0734615 | + | 0.127239i | ||||
\(731\) | 5.40015e15 | + | 9.35334e15i | 0.956887 | + | 1.65738i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −1.71682e15 | + | 2.97363e15i | −0.299678 | + | 0.519057i | −0.976062 | − | 0.217492i | \(-0.930212\pi\) |
0.676385 | + | 0.736549i | \(0.263546\pi\) | |||||||
\(734\) | 1.18678e14 | 0.0205610 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −7.40722e14 | −0.126423 | ||||||||
\(737\) | 1.00929e14 | − | 1.74813e14i | 0.0170979 | − | 0.0296145i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1.17677e15 | − | 2.03823e15i | −0.196403 | − | 0.340180i | 0.750957 | − | 0.660351i | \(-0.229593\pi\) |
−0.947359 | + | 0.320172i | \(0.896259\pi\) | |||||||
\(740\) | −2.80311e15 | + | 4.85513e15i | −0.464372 | + | 0.804316i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 8.50961e14 | + | 2.23038e14i | 0.138895 | + | 0.0364047i | ||||
\(743\) | 1.13067e16 | 1.83188 | 0.915940 | − | 0.401316i | \(-0.131447\pi\) | ||||
0.915940 | + | 0.401316i | \(0.131447\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1.99117e15 | + | 3.44882e15i | 0.317870 | + | 0.550567i | ||||
\(746\) | −3.91725e14 | − | 6.78488e14i | −0.0620751 | − | 0.107517i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −1.70824e15 | −0.266742 | ||||||||
\(749\) | 1.86383e15 | − | 1.88431e15i | 0.288905 | − | 0.292080i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 2.89693e15 | − | 5.01763e15i | 0.442505 | − | 0.766441i | −0.555370 | − | 0.831603i | \(-0.687423\pi\) |
0.997875 | + | 0.0651627i | \(0.0207566\pi\) | |||||||
\(752\) | −4.99420e14 | − | 8.65021e14i | −0.0757300 | − | 0.131168i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 9.39410e13 | − | 1.62711e14i | 0.0140382 | − | 0.0243149i | ||||
\(755\) | 1.14692e16 | 1.70147 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −3.69592e15 | −0.540374 | −0.270187 | − | 0.962808i | \(-0.587086\pi\) | ||||
−0.270187 | + | 0.962808i | \(0.587086\pi\) | |||||||
\(758\) | 1.55115e13 | − | 2.68667e13i | 0.00225151 | − | 0.00389973i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 2.99232e14 | + | 5.18285e14i | 0.0428088 | + | 0.0741471i | ||||
\(761\) | 7.85569e14 | − | 1.36065e15i | 0.111575 | − | 0.193254i | −0.804830 | − | 0.593505i | \(-0.797744\pi\) |
0.916406 | + | 0.400251i | \(0.131077\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.73503e15 | + | 6.33651e15i | 0.242896 | + | 0.887085i | ||||
\(764\) | −9.72223e15 | −1.35130 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 6.31746e14 | + | 1.09422e15i | 0.0865535 | + | 0.149915i | ||||
\(767\) | −2.33668e15 | − | 4.04725e15i | −0.317852 | − | 0.550536i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1.12892e16 | 1.51380 | 0.756902 | − | 0.653529i | \(-0.226712\pi\) | ||||
0.756902 | + | 0.653529i | \(0.226712\pi\) | |||||||
\(770\) | 1.46530e14 | − | 1.48140e14i | 0.0195086 | − | 0.0197230i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −7.07389e14 | + | 1.22523e15i | −0.0928460 | + | 0.160814i | ||||
\(773\) | 9.91548e14 | + | 1.71741e15i | 0.129219 | + | 0.223814i | 0.923374 | − | 0.383901i | \(-0.125420\pi\) |
−0.794155 | + | 0.607715i | \(0.792086\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.68537e15 | − | 2.91914e15i | 0.216538 | − | 0.375055i | ||||
\(776\) | 3.22770e15 | 0.411769 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −6.47695e14 | −0.0814672 | ||||||||
\(779\) | 1.71782e14 | − | 2.97535e14i | 0.0214546 | − | 0.0371605i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 6.12862e14 | + | 1.06151e15i | 0.0754713 | + | 0.130720i | ||||
\(782\) | −2.78876e14 | + | 4.83027e14i | −0.0341015 | + | 0.0590656i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −6.79781e15 | + | 4.02439e15i | −0.819654 | + | 0.485246i | ||||
\(785\) | −8.38678e15 | −1.00418 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −6.95413e15 | − | 1.20449e16i | −0.821073 | − | 1.42214i | −0.904884 | − | 0.425658i | \(-0.860043\pi\) |
0.0838114 | − | 0.996482i | \(-0.473291\pi\) | |||||||
\(788\) | −3.49705e15 | − | 6.05706e15i | −0.410022 | − | 0.710179i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −8.63399e14 | −0.0998304 | ||||||||
\(791\) | −9.09006e15 | − | 2.38252e15i | −1.04375 | − | 0.273568i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 4.12289e15 | − | 7.14105e15i | 0.466873 | − | 0.808648i | ||||
\(794\) | 3.57966e14 | + | 6.20016e14i | 0.0402559 | + | 0.0697252i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −2.91871e15 | + | 5.05535e15i | −0.323719 | + | 0.560699i | ||||
\(797\) | −6.82904e15 | −0.752210 | −0.376105 | − | 0.926577i | \(-0.622737\pi\) | ||||
−0.376105 | + | 0.926577i | \(0.622737\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −2.31875e15 | −0.251911 | ||||||||
\(800\) | −1.11976e15 | + | 1.93948e15i | −0.120818 | + | 0.209263i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −1.14914e14 | − | 1.99038e14i | −0.0122297 | − | 0.0211825i | ||||
\(803\) | −7.33390e14 | + | 1.27027e15i | −0.0775175 | + | 0.134264i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.11127e15 | + | 4.05848e15i | 0.115862 | + | 0.423142i | ||||
\(806\) | 4.68295e14 | 0.0484927 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 1.68662e15 | + | 2.92131e15i | 0.172288 | + | 0.298412i | ||||
\(809\) | −8.33703e15 | − | 1.44402e16i | −0.845852 | − | 1.46506i | −0.884879 | − | 0.465820i | \(-0.845759\pi\) |
0.0390274 | − | 0.999238i | \(-0.487574\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −5.16144e15 | −0.516602 | −0.258301 | − | 0.966065i | \(-0.583163\pi\) | ||||
−0.258301 | + | 0.966065i | \(0.583163\pi\) | |||||||
\(812\) | −1.00487e15 | − | 3.66990e15i | −0.0998969 | − | 0.364835i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 8.07784e13 | − | 1.39912e14i | 0.00792247 | − | 0.0137221i | ||||
\(815\) | −1.11309e16 | − | 1.92793e16i | −1.08433 | − | 1.87812i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.67251e15 | − | 2.89687e15i | 0.160748 | − | 0.278424i | ||||
\(818\) | −1.11834e15 | −0.106765 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 2.16522e15 | 0.203951 | ||||||||
\(821\) | 5.05873e15 | − | 8.76198e15i | 0.473319 | − | 0.819813i | −0.526214 | − | 0.850352i | \(-0.676389\pi\) |
0.999534 | + | 0.0305391i | \(0.00972241\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 3.99868e15 | + | 6.92593e15i | 0.369163 | + | 0.639409i | 0.989435 | − | 0.144978i | \(-0.0463111\pi\) |
−0.620272 | + | 0.784387i | \(0.712978\pi\) | |||||||
\(824\) | 2.20903e15 | − | 3.82616e15i | 0.202583 | − | 0.350884i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 1.48022e15 | + | 3.87967e14i | 0.133948 | + | 0.0351079i | ||||
\(827\) | 1.50295e16 | 1.35102 | 0.675512 | − | 0.737349i | \(-0.263923\pi\) | ||||
0.675512 | + | 0.737349i | \(0.263923\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −6.43760e15 | − | 1.11502e16i | −0.571050 | − | 0.989087i | −0.996459 | − | 0.0840857i | \(-0.973203\pi\) |
0.425409 | − | 0.905001i | \(-0.360130\pi\) | |||||||
\(830\) | 3.22610e14 | + | 5.58777e14i | 0.0284281 | + | 0.0492390i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 6.03180e15 | 0.524528 | ||||||||
\(833\) | 2.00394e14 | + | 1.83377e16i | 0.0173116 | + | 1.58415i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1.07210e16 | − | 1.85692e16i | 0.914025 | − | 1.58314i | ||||
\(836\) | 2.64534e14 | + | 4.58186e14i | 0.0224051 | + | 0.0388068i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 8.87952e14 | − | 1.53798e15i | 0.0742245 | − | 0.128561i | ||||
\(839\) | 1.90314e16 | 1.58045 | 0.790225 | − | 0.612817i | \(-0.209964\pi\) | ||||
0.790225 | + | 0.612817i | \(0.209964\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.03979e16 | −0.852252 | ||||||||
\(842\) | 9.00229e14 | − | 1.55924e15i | 0.0733055 | − | 0.126969i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −3.01510e13 | − | 5.22230e13i | −0.00242336 | − | 0.00419738i | ||||
\(845\) | −5.34978e15 | + | 9.26609e15i | −0.427193 | + | 0.739920i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −8.66074e15 | + | 8.75590e15i | −0.682647 | + | 0.690148i | ||||
\(848\) | −1.38459e16 | −1.08429 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 8.43163e14 | + | 1.46040e15i | 0.0651789 | + | 0.112893i | ||||
\(851\) | 1.63129e15 | + | 2.82548e15i | 0.125291 | + | 0.217010i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −5.80889e15 | −0.440427 | −0.220213 | − | 0.975452i | \(-0.570675\pi\) | ||||
−0.220213 | + | 0.975452i | \(0.570675\pi\) | |||||||
\(854\) | 7.13036e14 | + | 2.60409e15i | 0.0537147 | + | 0.196172i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 6.91255e14 | − | 1.19729e15i | 0.0514082 | − | 0.0890416i | ||||
\(857\) | −5.44606e15 | − | 9.43285e15i | −0.402428 | − | 0.697025i | 0.591591 | − | 0.806239i | \(-0.298500\pi\) |
−0.994018 | + | 0.109213i | \(0.965167\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 4.88936e15 | − | 8.46862e15i | 0.356689 | − | 0.617803i | −0.630717 | − | 0.776013i | \(-0.717239\pi\) |
0.987406 | + | 0.158210i | \(0.0505723\pi\) | |||||||
\(860\) | 2.10811e16 | 1.52810 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 2.80338e15 | 0.200628 | ||||||||
\(863\) | 3.21366e15 | − | 5.56622e15i | 0.228529 | − | 0.395823i | −0.728844 | − | 0.684680i | \(-0.759942\pi\) |
0.957372 | + | 0.288857i | \(0.0932752\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −2.43730e15 | − | 4.22153e15i | −0.171128 | − | 0.296402i | ||||
\(866\) | 1.33201e15 | − | 2.30710e15i | 0.0929305 | − | 0.160960i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 6.66940e15 | − | 6.74268e15i | 0.459440 | − | 0.464488i | ||||
\(869\) | −1.53890e15 | −0.105342 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 8.56144e14 | + | 1.48288e15i | 0.0578691 | + | 0.100232i | ||||
\(872\) | 1.71349e15 | + | 2.96785e15i | 0.115091 | + | 0.199343i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 1.72744e14 | 0.0114575 | ||||||||
\(875\) | −6.55886e15 | − | 1.71909e15i | −0.432299 | − | 0.113306i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1.22064e16 | + | 2.11421e16i | −0.794491 | + | 1.37610i | 0.128670 | + | 0.991687i | \(0.458929\pi\) |
−0.923162 | + | 0.384412i | \(0.874404\pi\) | |||||||
\(878\) | −7.93877e14 | − | 1.37504e15i | −0.0513492 | − | 0.0889394i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −1.63977e15 | + | 2.84016e15i | −0.104743 | + | 0.181421i | ||||
\(881\) | 2.26230e16 | 1.43609 | 0.718045 | − | 0.695996i | \(-0.245037\pi\) | ||||
0.718045 | + | 0.695996i | \(0.245037\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 2.40396e14 | 0.0150711 | 0.00753554 | − | 0.999972i | \(-0.497601\pi\) | ||||
0.00753554 | + | 0.999972i | \(0.497601\pi\) | |||||||
\(884\) | 7.24523e15 | − | 1.25491e16i | 0.451403 | − | 0.781853i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −1.25367e15 | − | 2.17141e15i | −0.0771429 | − | 0.133615i | ||||
\(887\) | −7.90944e15 | + | 1.36996e16i | −0.483689 | + | 0.837773i | −0.999825 | − | 0.0187334i | \(-0.994037\pi\) |
0.516136 | + | 0.856507i | \(0.327370\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.51301e16 | − | 3.96563e15i | −0.913866 | − | 0.239526i | ||||
\(890\) | −3.09813e15 | −0.185975 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −2.54200e15 | − | 4.40287e15i | −0.150719 | − | 0.261054i | ||||
\(893\) | 3.59075e14 | + | 6.21937e14i | 0.0211594 | + | 0.0366491i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 2.97748e16 | 1.73309 | ||||||||
\(896\) | −5.89171e15 | + | 5.95644e15i | −0.340837 | + | 0.344582i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −2.40389e14 | + | 4.16366e14i | −0.0137371 | + | 0.0237934i | ||||
\(899\) | 2.24649e15 | + | 3.89103e15i | 0.127593 | + | 0.220997i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.60713e16 | + | 2.78362e16i | −0.901703 | + | 1.56180i | ||||
\(902\) | −6.23960e13 | −0.00347953 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −4.90180e15 | −0.270041 | ||||||||
\(905\) | −3.40185e15 | + | 5.89218e15i | −0.186272 | + | 0.322633i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −2.57501e15 | − | 4.46004e15i | −0.139296 | − | 0.241267i | 0.787934 | − | 0.615759i | \(-0.211151\pi\) |
−0.927230 | + | 0.374492i | \(0.877817\pi\) | |||||||
\(908\) | −1.22593e16 | + | 2.12337e16i | −0.659163 | + | 1.14170i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 4.66783e14 | + | 1.70474e15i | 0.0247963 | + | 0.0905590i | ||||
\(911\) | −2.54507e16 | −1.34384 | −0.671922 | − | 0.740622i | \(-0.734531\pi\) | ||||
−0.671922 | + | 0.740622i | \(0.734531\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 5.75013e14 | + | 9.95951e14i | 0.0299977 | + | 0.0519576i | ||||
\(914\) | −5.17238e14 | − | 8.95882e14i | −0.0268217 | − | 0.0464565i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 8.77750e15 | 0.449724 | ||||||||
\(917\) | 1.34657e15 | − | 1.36136e15i | 0.0685799 | − | 0.0693334i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −3.49711e15 | + | 6.05718e15i | −0.175984 | + | 0.304814i | −0.940502 | − | 0.339789i | \(-0.889644\pi\) |
0.764517 | + | 0.644604i | \(0.222978\pi\) | |||||||
\(920\) | 1.09747e15 | + | 1.90088e15i | 0.0548986 | + | 0.0950872i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 6.63072e14 | − | 1.14848e15i | 0.0327749 | − | 0.0567677i | ||||
\(923\) | −1.03974e16 | −0.510876 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 9.86420e15 | 0.478942 | ||||||||
\(926\) | −1.38674e15 | + | 2.40191e15i | −0.0669322 | + | 0.115930i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −1.49257e15 | − | 2.58521e15i | −0.0711904 | − | 0.123305i | ||||
\(929\) | −6.32951e15 | + | 1.09630e16i | −0.300112 | + | 0.519810i | −0.976161 | − | 0.217047i | \(-0.930358\pi\) |
0.676049 | + | 0.736857i | \(0.263691\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 4.88751e15 | − | 2.89347e15i | 0.229015 | − | 0.135580i | ||||
\(932\) | 3.44420e16 | 1.60435 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 2.68895e14 | + | 4.65740e14i | 0.0123787 | + | 0.0214405i | ||||
\(935\) | 3.80662e15 | + | 6.59325e15i | 0.174211 | + | 0.301742i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 2.80207e16 | 1.26739 | 0.633697 | − | 0.773582i | \(-0.281537\pi\) | ||||
0.633697 | + | 0.773582i | \(0.281537\pi\) | |||||||
\(938\) | −5.42341e14 | − | 1.42148e14i | −0.0243869 | − | 0.00639185i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −2.26298e15 | + | 3.91959e15i | −0.100572 | + | 0.174196i | ||||
\(941\) | −2.38780e15 | − | 4.13578e15i | −0.105500 | − | 0.182732i | 0.808442 | − | 0.588576i | \(-0.200311\pi\) |
−0.913943 | + | 0.405844i | \(0.866978\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 6.30033e14 | − | 1.09125e15i | 0.0275137 | − | 0.0476551i | ||||
\(944\) | −2.40846e16 | −1.04567 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −6.07501e14 | −0.0260703 | ||||||||
\(947\) | 1.48624e16 | − | 2.57425e16i | 0.634110 | − | 1.09831i | −0.352593 | − | 0.935777i | \(-0.614700\pi\) |
0.986703 | − | 0.162534i | \(-0.0519668\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −6.22110e15 | − | 1.07753e16i | −0.262363 | − | 0.454427i | ||||
\(950\) | 2.61140e14 | − | 4.52307e14i | 0.0109495 | − | 0.0189650i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 2.52632e15 | + | 9.22641e15i | 0.104709 | + | 0.382410i | ||||
\(953\) | −4.28873e15 | −0.176733 | −0.0883665 | − | 0.996088i | \(-0.528165\pi\) | ||||
−0.0883665 | + | 0.996088i | \(0.528165\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 2.16648e16 | + | 3.75246e16i | 0.882545 | + | 1.52861i | ||||
\(956\) | 3.07206e14 | + | 5.32096e14i | 0.0124426 | + | 0.0215512i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −3.66890e15 | −0.146901 | ||||||||
\(959\) | 1.15626e16 | + | 4.22281e16i | 0.460315 | + | 1.68112i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 7.10488e15 | − | 1.23060e16i | 0.279626 | − | 0.484327i | ||||
\(962\) | 6.85216e14 | + | 1.18683e15i | 0.0268142 | + | 0.0464435i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 1.68085e15 | − | 2.91131e15i | 0.0650286 | − | 0.112633i | ||||
\(965\) | 6.30533e15 | 0.242553 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 8.30400e15 | 0.315822 | 0.157911 | − | 0.987453i | \(-0.449524\pi\) | ||||
0.157911 | + | 0.987453i | \(0.449524\pi\) | |||||||
\(968\) | −3.21209e15 | + | 5.56350e15i | −0.121471 | + | 0.210394i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −3.56743e15 | − | 6.17897e15i | −0.133386 | − | 0.231032i | ||||
\(971\) | −1.68239e16 | + | 2.91399e16i | −0.625491 | + | 1.08338i | 0.362954 | + | 0.931807i | \(0.381768\pi\) |
−0.988446 | + | 0.151576i | \(0.951565\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 3.14771e15 | + | 8.25019e14i | 0.115711 | + | 0.0303280i | ||||
\(974\) | 4.70221e15 | 0.171881 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −2.12476e16 | − | 3.68020e16i | −0.767956 | − | 1.33014i | ||||
\(977\) | −1.98072e16 | − | 3.43071e16i | −0.711875 | − | 1.23300i | −0.964152 | − | 0.265349i | \(-0.914513\pi\) |
0.252277 | − | 0.967655i | \(-0.418820\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −5.52204e15 | −0.196243 | ||||||||
\(980\) | 3.11934e16 | + | 1.75579e16i | 1.10235 | + | 0.620481i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −2.01220e15 | + | 3.48523e15i | −0.0703166 | + | 0.121792i | ||||
\(983\) | 1.53479e16 | + | 2.65834e16i | 0.533342 | + | 0.923775i | 0.999242 | + | 0.0389378i | \(0.0123974\pi\) |
−0.465900 | + | 0.884838i | \(0.654269\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1.55855e16 | + | 2.69949e16i | −0.535576 | + | 0.927646i | ||||
\(986\) | −2.24777e15 | −0.0768118 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −4.48791e15 | −0.151663 | ||||||||
\(989\) | 6.13414e15 | − | 1.06246e16i | 0.206146 | − | 0.357055i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −7.01280e15 | − | 1.21465e16i | −0.233070 | − | 0.403689i | 0.725640 | − | 0.688075i | \(-0.241544\pi\) |
−0.958710 | + | 0.284385i | \(0.908211\pi\) | |||||||
\(992\) | 3.72023e15 | − | 6.44363e15i | 0.122958 | − | 0.212969i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 2.39413e15 | − | 2.42043e15i | 0.0782568 | − | 0.0791167i | ||||
\(995\) | 2.60160e16 | 0.845694 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1.01222e16 | + | 1.75321e16i | 0.325424 | + | 0.563651i | 0.981598 | − | 0.190959i | \(-0.0611596\pi\) |
−0.656174 | + | 0.754610i | \(0.727826\pi\) | |||||||
\(998\) | −2.34893e15 | − | 4.06847e15i | −0.0751023 | − | 0.130081i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 63.12.e.b.37.4 | 12 | ||
3.2 | odd | 2 | 7.12.c.a.2.3 | ✓ | 12 | ||
7.4 | even | 3 | inner | 63.12.e.b.46.4 | 12 | ||
12.11 | even | 2 | 112.12.i.c.65.6 | 12 | |||
21.2 | odd | 6 | 49.12.a.g.1.4 | 6 | |||
21.5 | even | 6 | 49.12.a.f.1.4 | 6 | |||
21.11 | odd | 6 | 7.12.c.a.4.3 | yes | 12 | ||
21.17 | even | 6 | 49.12.c.i.18.3 | 12 | |||
21.20 | even | 2 | 49.12.c.i.30.3 | 12 | |||
84.11 | even | 6 | 112.12.i.c.81.6 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
7.12.c.a.2.3 | ✓ | 12 | 3.2 | odd | 2 | ||
7.12.c.a.4.3 | yes | 12 | 21.11 | odd | 6 | ||
49.12.a.f.1.4 | 6 | 21.5 | even | 6 | |||
49.12.a.g.1.4 | 6 | 21.2 | odd | 6 | |||
49.12.c.i.18.3 | 12 | 21.17 | even | 6 | |||
49.12.c.i.30.3 | 12 | 21.20 | even | 2 | |||
63.12.e.b.37.4 | 12 | 1.1 | even | 1 | trivial | ||
63.12.e.b.46.4 | 12 | 7.4 | even | 3 | inner | ||
112.12.i.c.65.6 | 12 | 12.11 | even | 2 | |||
112.12.i.c.81.6 | 12 | 84.11 | even | 6 |